Engee documentation

Rotational Mechanical Converter (MA)

Interface (converter) between humid air and mechanical rotary networks.

blockType: AcausalFoundation.MoistAir.Elements.RotationalMechanicalConverter

rotational mechanical converter (ma)

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Rotational Mechanical Converter (MA)

Description

Block Rotational Mechanical Converter (MA) It is an interface between a humid air network and a mechanical rotary network. The unit converts humid air pressure into mechanical torque and vice versa. It can be used as a base for rotary actuators.

The volume of humid air in the converter changes during operation. The pressure and temperature vary depending on the compressibility and heat capacity of the volume of moist air. Liquid water condenses from the volume of moist air when it reaches saturation.

Parameter Mechanical orientation determines whether an increase in the volume of humid air leads to a positive or negative rotation of port R relative to port C.

Port A is the humid air port corresponding to the input of the converter. Ports R and C are mechanical rotary ports corresponding to the shaft and housing respectively.

Subscript indexes:

  • — properties of dry air, water vapor, and impurity moist air, respectively;

  • — water vapor at saturation;

  • — the appropriate port;

  • — properties of the internal volume of humid air.

Characteristics of the simulated system:

  • — mass consumption;

  • — the rate of energy consumption;

  • — heat consumption;

  • — pressure;

  • — density;

  • — universal gas constant;

  • — the volume of moist air inside the converter;

  • — specific heat capacity at constant volume;

  • — specific enthalpy;

  • — specific internal energy;

  • — mass fraction ( — specific humidity, which is otherwise called the mass fraction of water vapor);

  • — molar fraction;

  • — relative humidity;

  • — humidity coefficient;

  • — temperature;

  • — the time.

The net consumption of moist air in the tank is:

,

,

,

,

where

  • — condensation rate;

  • — the rate of condensate energy loss;

  • — the rate of energy addition from sources of moisture and impurity gases;

  • and — massive flow of water and air through the port S.

Values and They are determined by sources of moisture and impurity gas connected to the S port of the converter.

If the port is not in use, then the terms of the equation with the subscript corresponding to the port name are equal to .

The conservation of water vapor mass relates the mass flow rate of water vapor to the dynamics of the humidity level in the internal volume of humid air:

.

Similarly, the conservation of impurity gas mass relates the mass flow rate of impurity gas to the dynamics of the impurity gas level in the internal volume of humid air:

.

The conservation of the mass of the mixture relates the mass flow rate of the mixture to the dynamics of pressure, temperature, and mass fractions of the internal volume of moist air.:

,

where — the rate of change in the volume of the converter.

Finally, the law of conservation of energy relates the rate of energy flow to the dynamics of pressure, temperature, and mass fractions of the internal volume of humid air.:

.

The equation of state relates the density of a mixture to pressure and temperature:

.

The universal gas constant of the mixture is:

.

The volume of the converter depends on the rotation of the shaft:

.

where

  • — the volume of liquid at which the angle of rotation of the shaft is 0;

  • — volumetric displacement of the shaft;

  • — angle of rotation of the shaft;

  • — coefficient of mechanical orientation. If the parameter Mechanical orientation set to the value Pressure at A causes positive rotation of R relative to C Then , otherwise .

The rotation of the shaft is zero if the volume of moist air inside the converter is equal to . Then, depending on the value of the parameter Mechanical orientation, the following is true:

  • If it is set to Pressure at A causes positive rotation of R relative to C, then the rotation of the interface increases when the volume of moist air increases compared to the dead volume.

  • If it is set to Pressure at A causes negative rotation of R relative to C, the rotation of the interface decreases when the volume of moist air increases compared to the dead volume.

The equation describing the equilibrium of torques on the converter:

,

where

  • — torque from port R to port C;

  • — atmospheric pressure.

The gas and thermal resistances in the converter are not modeled:

,

.

When the air reaches saturation, moisture condensation may occur. The specific humidity at saturation is:

,

where

  • — relative humidity of the air at saturation (usually 1);

  • — saturation pressure of water vapor, estimated at .

The condensation rate is:

,

where — parameter value Condensation time constant.

The condensate is subtracted from the volume of humid air, as shown in the conservation equations. The energy associated with the condensate is:

,

where — the specific enthalpy of vaporization, estimated at .

Other amounts of moisture and impurity gas are related as follows:

,

,

,

,

.

Assumptions and limitations

  • The walls of the transducer are ideally rigid.

  • The gas resistance between the input and the inside of the converter is negligible.

  • The thermal resistance between the H port and the volume of humid air is not modeled.

  • The mobile interface works losslessly.

  • The block does not simulate such mechanical effects as hard stop, friction and inertia.

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# A — humid air inlet
humid air

Details

Humid air port, corresponds to the inverter input.

Program usage name

port

# C — hull
translational mechanics

Details

Mechanical progressive port, corresponds to the inverter housing.

Program usage name

case_flange

# R — shaft
`rotational mechanics

Details

Mechanical progressive port, corresponds to a shaft.

Program usage name

rod_flange

# H — internal temperature
`heat

Details

Heat port related to the temperature of the moist air mixture inside the converter.

Program usage name

thermal_port

# S — addition or removal of moisture and impurity gases
`moist air

Details

Connect this port to the S port of the unit from the library Moisture & Trace Gas Sources to add or remove moisture and impure gases.

Dependencies

To use this port, set the Moisture and trace gas source parameters to Controlled.

Program usage name

source_port

Output

# W — condensation rate, kg/s
scalar

Details

An output port that measures the condensation rate in the inverter.

Data types

Float64.
Complex numbers support

No

# F — vector signal containing data on pressure, temperature, humidity and level of impurity gases
`vector'

Details

An output port that outputs a vector signal. The vector contains the results of pressure (Pa), temperature (K), humidity level and impurity gas level measurements inside the component.

Data types

Float64.
Complex numbers support

No

Input

# q — rotation of port R relative to port C, rad
scalar

Details

Input port that transmits position information. Connect this port to the q port of the position sensor.

Dependencies

To use this port, set the parameters Interface rotation to . Provide input signal.

Data types

Float64.
Complex numbers support

No

Parameters

Main

# Mechanical orientation — Select the orientation of the inverter
Pressure at A causes positive rotation of R relative to C | Pressure at A causes negative rotation of R relative to C

Details

Select the movement of the shaft in relation to the volume of moist air inside the converter:

  • Pressure at A causes positive rotation of R relative to C - An increase in the moist air volume results in a positive rotation of port R relative to port C.

  • Pressure at A causes negative rotation of R relative to C - Increase in the volume of humid air leads to a negative rotation of port R relative to port C.

Values

Pressure at A causes positive rotation of R relative to C | Pressure at A causes negative rotation of R relative to C
Default value

Pressure at A causes positive rotation of R relative to C
Program usage name

orientation
Evaluatable

No

# Initial interface rotation — rotational displacement of port R relative to port C at the beginning of modelling
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

Rotational displacement of port R relative to port C at the start of the simulation. The value 0 corresponds to an initial volume of moist air equal to Dead volume.

Dependencies

To use the parameter, set the parameter Interface rotation to the value of Calculate from angular velocity of port R relative to port C:

  • If Mechanical orientation - Pressure at A causes positive rotation of R relative to C, then the value of the parameters must be greater than or equal to 0.

  • If Mechanical orientation - Pressure at A causes negative rotation of R relative to C, the value of the parameters must be less than or equal to 0.

Units

rad | deg | rev | mrad | arcsec | arcmin | gon
Default value

0.0 rad
Program usage name

delta_phi_start
Evaluatable

Yes

# Interface volume displacement — volume of transported humid air per unit of rotation
m^3/rad | mm^3/rad | cm^3/rad | km^3/rad | m^3/deg | cm^3/rev | m^3/rev | l/rad | l/rev | in^3/rad | ft^3/rad | gal/rad | igal/rad | in^3/deg | in^3/rev | gal/rev

Details

Volume of moist air displaced per unit revolution of the shaft.

Units

m^3/rad | mm^3/rad | cm^3/rad | km^3/rad | m^3/deg | cm^3/rev | m^3/rev | l/rad | l/rev | in^3/rad | ft^3/rad | gal/rad | igal/rad | in^3/deg | in^3/rev | gal/rev
Default value

0.01 m^3/rad
Program usage name

volume_displacement
Evaluatable

Yes

# Dead volume — Humid air volume at shaft angle 0
m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3

Details

Volume of moist air at shaft angle of rotation equal to 0.

Units

m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3
Default value

1.e-5 m^3
Program usage name

dead_volume
Evaluatable

Yes

# Cross-sectional area at port A — area normal to the flow cross-section at the inlet to the transducer
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the converter inlet in the direction normal to the wet air flow path.

Units

m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Default value

0.01 m^2
Program usage name

port_area
Evaluatable

Yes

# Environment pressure specification — method of setting the ambient pressure
Atmospheric pressure | Specified pressure

Details

Select the ambient pressure setting method:

  • Atmospheric pressure - atmospheric pressure is used.

  • Specified pressure - set the value with the parameters Environment pressure.

Values

Atmospheric pressure | Specified pressure
Default value

Atmospheric pressure
Program usage name

environment_type
Evaluatable

No

# Environment pressure — outside pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Pressure outside the converter acting against the pressure of the moist volume of air in the converter. A value of 0 means that the gas in the converter is expanding into a vacuum.

Dependencies

To use this parameter, set the parameters Environment pressure specification to the value of Specified pressure.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

0.101325 MPa
Program usage name

environment_pressure
Evaluatable

Yes

Moisture and Trace Gas

# Relative humidity at saturation — Relative humidity above which condensation occurs

Details

Relative humidity above which condensation occurs.

Default value

1.0
Program usage name

RH_saturation
Evaluatable

Yes

# Condensation time constant — condensation time constant
s | ns | us | ms | min | hr | d

Details

A time scale factor characterising the time period for the return of the supersaturated volume of moist air to the saturation level due to condensation of excess moisture.

Units

s | ns | us | ms | min | hr | d
Default value

0.001 s
Program usage name

condensation_time_constant
Evaluatable

Yes

# Moisture and trace gas source — source of moisture and impurity gases
None | Constant | Controlled

Details

This parameter controls the usage of the S port and provides the following options for modelling moisture and impurity gas levels within the unit:

  • None - no impurity gas is introduced into or extracted from the block. The S port is hidden. This value is used by default.

  • Constant - moisture and impurity gas are introduced into or extracted from the block at a constant rate. The same parameters as in the Moisture Source (MA) and Trace Gas Source (MA) units are available in the unit settings. The S port is hidden.

  • Controlled - Moisture and impurity gas are introduced into or removed from the block at a time-varying rate. Port S is open. Units Moisture Source (MA) and Trace Gas Source (MA) are connected to this port.

Values

None | Constant | Controlled
Default value

None
Program usage name

moisture_trace_gas_source
Evaluatable

No

# Moisture added or removed — add or remove moisture in the form of water vapour or water
Vapor | Liquid

Details

Select whether the unit adds or removes moisture as water vapour or water:

  • Vapor - the enthalpy of added or removed moisture corresponds to the enthalpy of water vapour, which is greater than the enthalpy of water.

  • Liquid - the enthalpy of added or removed moisture corresponds to the enthalpy of water, which is less than the enthalpy of water vapour.

Dependencies

To use this parameter, set the parameter Moisture and trace gas source to . Constant.

Values

Vapor | Liquid
Default value

Vapor
Program usage name

moisture_source_phase
Evaluatable

No

# Rate of added moisture — constant mass flow rate through the source
kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s

Details

Mass flow rate of moisture through the source.

A positive value adds moisture to the connected humid air network. A negative value removes moisture from this network.

Dependencies

To use this parameter, set the parameter Moisture and trace gas source to Constant.

Units

kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s
Default value

0.0 kg/s
Program usage name

moisture_mass_flow
Evaluatable

Yes

# Added moisture temperature specification — Moisture temperature setting method
Atmospheric temperature | Specified temperature

Details

Selects the method for setting the moisture temperature:

  • Atmospheric temperature - the atmospheric temperature set by the unit Moist Air Properties (MA), connected to the circuit, is used.

  • Specified temperature - the value is set with the parameters Temperature of added moisture.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Values

Atmospheric temperature | Specified temperature
Default value

Atmospheric temperature
Program usage name

moisture_temperature_type
Evaluatable

No

# Temperature of added moisture — moisture temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

Enter the moisture temperature. This temperature remains constant during the simulation. The unit only uses this value to estimate the specific enthalpy of added moisture. The specific enthalpy of removed moisture is determined based on the temperature of the connected humid air network.

Dependencies

To use this parameter, set the parameters Added moisture temperature specification to Specified temperature.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

293.15 K
Program usage name

moisture_temperature
Evaluatable

Yes

# Rate of added trace gas — constant mass flow rate through the source
kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s

Details

Reflects the mass flow rate of impurity gas through the source. A positive value adds impurity gas to the connected humid air volume, a negative value removes it.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Units

kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s
Default value

0.0 kg/s
Program usage name

trace_gas_mass_flow
Evaluatable

Yes

# Added trace gas temperature specification — method for setting the impurity gas temperature
Atmospheric temperature | Specified temperature

Details

Selection of the impurity gas temperature setting method:

  • Atmospheric temperature - the atmospheric temperature set by the Moist Air Properties (MA) unit connected to the mains is used.

  • Specified temperature - the value is set with the parameters Temperature of added trace gas.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Values

Atmospheric temperature | Specified temperature
Default value

Atmospheric temperature
Program usage name

trace_gas_temperature_type
Evaluatable

No

# Temperature of added trace gas — impurity gas temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

Enter the desired temperature of the impurity gas to be added. This temperature remains constant during the simulation. The unit only uses this value to estimate the specific enthalpy of the added impurity gas. The specific enthalpy of the removed impurity gas is determined based on the temperature of the connected wet air volume.

Dependencies

To use this parameter, set the parameters Added trace gas temperature specification to . Specified temperature.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

293.15 K
Program usage name

trace_gas_temperature
Evaluatable

Yes